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A136412 a(n) = (5*4^n + 1)/3. 11
2, 7, 27, 107, 427, 1707, 6827, 27307, 109227, 436907, 1747627, 6990507, 27962027, 111848107, 447392427, 1789569707, 7158278827, 28633115307, 114532461227, 458129844907, 1832519379627, 7330077518507, 29320310074027 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
An Engel expansion of 4/5 to the base b := 4/3 as defined in A181565, with the associated series expansion 4/5 = b/2 + b^2/(2*7) + b^3/(2*7*27) + b^4/(2*7*27*107) + .... Cf. A199115 and A140660. - Peter Bala, Oct 29 2013
LINKS
FORMULA
a(n) = 4*a(n-1) - 1.
a(n) = A199115(n)/3.
O.g.f.: (2-3*x)/((1-x)*(1-4*x)). - R. J. Mathar, Apr 04 2008
a(n) = 5*a(n-1) - 4*a(n-2). - Vincenzo Librandi, Nov 04 2011
E.g.f.: (1/3)*(5*exp(4*x) + exp(x)). - G. C. Greubel, Jan 19 2023
MATHEMATICA
LinearRecurrence[{5, -4}, {2, 7}, 31] (* G. C. Greubel, Jan 19 2023 *)
PROG
(Magma) [(5*4^n+1)/3: n in [0..30]]; // Vincenzo Librandi, Nob 04 2011
(Haskell)
a136412 = (`div` 3) . (+ 1) . (* 5) . (4 ^)
-- Reinhard Zumkeller, Jun 17 2012
(PARI) a(n)=(5*4^n+1)/3 \\ Charles R Greathouse IV, Oct 07 2015
(SageMath) [(5*4^n+1)/3 for n in range(31)] # G. C. Greubel, Jan 19 2023
CROSSREFS
Sequences of the form (m*4^n + 1)/3: A007583 (m=2), this sequence (m=5), A199210 (m=11), A199210 (m=11), A206373 (m=14).
Sequence in context: A150592 A150593 A024429 * A360149 A192417 A150594
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Mar 31 2008
EXTENSIONS
Formula in definition and more terms from R. J. Mathar, Apr 04 2008
STATUS
approved

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Last modified March 4 16:44 EST 2024. Contains 370532 sequences. (Running on oeis4.)